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Generalized convolution

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  • Tenreiro Machado, J.A.

Abstract

The paper revisits the convolution operator and addresses its generalization in the perspective of fractional calculus. Two examples demonstrate the feasibility of the concept using analytical expressions and the inverse Fourier transform, for real and complex orders. Two approximate calculation schemes in the time domain are also tested.

Suggested Citation

  • Tenreiro Machado, J.A., 2015. "Generalized convolution," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 34-39.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:34-39
    DOI: 10.1016/j.amc.2014.09.082
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    References listed on IDEAS

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    1. Svenkeson, A. & Beig, M.T. & Turalska, M. & West, B.J. & Grigolini, P., 2013. "Fractional trajectories: Decorrelation versus friction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5663-5672.
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